Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets

In this article, a nonlocal plate model which accounts for the small scale effects is developed to study the vibrational characteristics of multi-layered graphene sheets with different boundary conditions embedded in an elastic medium. On the basis of the constitutive equations of nonlocal elasticity, the Mindlin-type equations of motion coupled together through the van der Waals interaction are derived. The finite element method is implemented to discretize the set of coupled field equations. The influences of the small scale parameter, length of a square plate and the elastic medium on the mechanical behavior of multi-layered graphene sheets are investigated. The results obtained from the present numerical solution have been compared with the existing data from the literature and good agreement has been found.